1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
|
# Computes the diffraction orders of a 2D binary grating with
# triangular lattice using a rectangular supercell and verifies
# that only the diffraction orders of the actual unit cell
# produce non-zero power (up to discretization error)
import math
import numpy as np
import meep as mp
resolution = 100 # pixels/μm
ng = 1.5
glass = mp.Medium(index=ng)
wvl = 0.5 # wavelength
fcen = 1 / wvl
# rectangular supercell
sx = 1.0
sy = np.sqrt(3)
dpml = 1.0 # PML thickness
dsub = 2.0 # substrate thickness
dair = 2.0 # air padding
hcyl = 0.5 # cylinder height
rcyl = 0.1 # cylinder radius
sz = dpml + dsub + hcyl + dair + dpml
cell_size = mp.Vector3(sx, sy, sz)
boundary_layers = [mp.PML(thickness=dpml, direction=mp.Z)]
# periodic boundary conditions
k_point = mp.Vector3()
src_pt = mp.Vector3(0, 0, -0.5 * sz + dpml)
sources = [
mp.Source(
src=mp.GaussianSource(fcen, fwidth=0.1 * fcen),
size=mp.Vector3(sx, sy, 0),
center=src_pt,
component=mp.Ex,
)
]
substrate = [
mp.Block(
size=mp.Vector3(mp.inf, mp.inf, dpml + dsub),
center=mp.Vector3(0, 0, -0.5 * sz + 0.5 * (dpml + dsub)),
material=glass,
)
]
cyl_grating = [
mp.Cylinder(
center=mp.Vector3(0, 0, -0.5 * sz + dpml + dsub + 0.5 * hcyl),
radius=rcyl,
height=hcyl,
material=glass,
),
mp.Cylinder(
center=mp.Vector3(0.5 * sx, 0.5 * sy, -0.5 * sz + dpml + dsub + 0.5 * hcyl),
radius=rcyl,
height=hcyl,
material=glass,
),
mp.Cylinder(
center=mp.Vector3(-0.5 * sx, 0.5 * sy, -0.5 * sz + dpml + dsub + 0.5 * hcyl),
radius=rcyl,
height=hcyl,
material=glass,
),
mp.Cylinder(
center=mp.Vector3(-0.5 * sx, -0.5 * sy, -0.5 * sz + dpml + dsub + 0.5 * hcyl),
radius=rcyl,
height=hcyl,
material=glass,
),
mp.Cylinder(
center=mp.Vector3(0.5 * sx, -0.5 * sy, -0.5 * sz + dpml + dsub + 0.5 * hcyl),
radius=rcyl,
height=hcyl,
material=glass,
),
]
geometry = substrate + cyl_grating
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
sources=sources,
geometry=geometry,
boundary_layers=boundary_layers,
k_point=k_point,
)
tran_pt = mp.Vector3(0, 0, 0.5 * sz - dpml)
tran_flux = sim.add_mode_monitor(
fcen, 0, 1, mp.ModeRegion(center=tran_pt, size=mp.Vector3(sx, sy, 0))
)
sim.run(until_after_sources=mp.stop_when_fields_decayed(20, mp.Ex, src_pt, 1e-6))
# diffraction order of unit cell (triangular lattice)
mx = 0
my = 1
# check: for diffraction orders of supercell for which
# nx = mx and ny = -mx + 2*my and thus
# only even orders should produce nonzero power
nx = mx
for ny in range(4):
kz2 = fcen**2 - (nx / sx) ** 2 - (ny / sy) ** 2
if kz2 > 0:
res = sim.get_eigenmode_coefficients(
tran_flux, mp.DiffractedPlanewave((nx, ny, 0), mp.Vector3(0, 1, 0), 1, 0)
)
t_coeffs = res.alpha
tran = abs(t_coeffs[0, 0, 0]) ** 2
print(f"order:, {nx}, {ny}, {tran:.5f}")
|
